public class UnionFind2 implements UF {
    private int[] parent;

    public UnionFind2(int size) {
        parent = new int[size];

        for (int i = 0; i < size; i ++)
            parent[i] = i;
    }

    @Override
    public int getSize() {
        return parent.length;
    }

    private int find(int p) {
        if (p < 0 || p >= parent.length)
            throw new IllegalArgumentException("p is out of bound.");
        
        while (p != parent[p])
            p = parent[p];
        return p;
    }

    @Override
    public boolean isConnected(int p, int q) {
        return find(p) == find(q);
    }

    @Override
    public void unionElements(int p, int q) {
        int pRoot = find(p);
        int qRoot = find(q);

        if (pRoot == qRoot)
            return;

        parent[pRoot] = parent[qRoot];
    }
}